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The Journal of Neuroscience, November 15, 1999, 19(22):10074-10081
Neural Representation of a Rhythm Depends on Its Interval Ratio
Katsuyuki Sakai1, 2, Okihide Hikosaka1, Satoru Miyauchi3, Ryousuke Takino4, Tomoe Tamada5, Nobue Kobayashi Iwata2, and Mathew Nielsen3 1 Department of Physiology, Juntendo University School of Medicine, Tokyo 113-0033, Japan, 2 Department of Neurology, Division of Neuroscience, Graduate School of Medicine, University of Tokyo, Tokyo 113-0033, Japan, 3 Communications Research Laboratory, Kobe 651-24, Japan, 4 Shiraume Gakuen College, Tokyo 187-8570, Japan, and 5 Exploratory Research for Advanced Technology, Japan Science and Technology Corporation, Kyoto 619-02, Japan
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Rhythm is determined solely by the relationship between the time intervals of a series of events. Psychological studies have proposed two types of rhythm representation depending on the interval ratio of the rhythm: metrical and nonmetrical representation for rhythms formed with small integer ratios and noninteger ratios, respectively. We used functional magnetic resonance imaging to test whether there are two neural representations of rhythm depending on the interval ratio. The subjects performed a short-term memory task for a seven-tone rhythm sequence, which was formed with 1:2:4, 1:2:3, or 1:2.5:3.5 ratios. The brain activities during the memory delay period were measured and compared with those during the retention of a control tone sequence, which had constant intertone intervals. The results showed two patterns of brain activations; the left premotor and parietal areas and right cerebellar anterior lobe were active for 1:2:4 and 1:2:3 rhythms, whereas the right prefrontal, premotor, and parietal areas together with the bilateral cerebellar posterior lobe were active for 1:2.5:3.5 rhythm. Analysis on individual subjects revealed that these activation patterns depended on the ratio of the rhythms that were produced by the subjects rather than the ratio of the presented rhythms, suggesting that the observed activations reflected the internal representation of rhythm. These results suggested that there are two neural representations for rhythm depending on the interval ratio, which correspond to metrical and nonmetrical representations.
Key words: rhythm; short-term memory; metrical representation; nonmetrical representation; interval ratio; cerebellar anterior lobe; cerebellar posterior lobe; right hemisphere; left hemisphere
INTRODUCTION
Rhythm is a flow of time, a series of time intervals marked off by the onsets of sensory or motor events, such as tones, flashes of lights, and steps in dances. Thus, rhythm is a supramodal entity that is determined solely by time information. The fact that we can recognize, discriminate, and reproduce a large number of rhythms suggests that individual rhythms can be internally represented, but its neural mechanism has not been well understood.
To date, most of the studies on neural processing of rhythm have been based on brain-damaged patients. Rhythm processing can be selectively impaired without any deficit in melody processing, suggesting the presence of a neural system specialized for rhythm (Peretz and Kolinsky, 1993
). A number of studies have shown that the left cerebral hemisphere is involved in rhythm processing (Gordon and Bogen, 1974
The inconsistency among these studies may be attributable to the fact that they used actual music as a test stimulus, which contains various types of rhythms. In this respect, previous psychological studies have identified an important constraint. Essens (1986)
In the present study, we have used functional magnetic resonance imaging (fMRI) to identify the neural representation of rhythm and tested whether there are two types of neural representation of rhythm, which correspond to metrical and nonmetrical representations. For this purpose, we used rhythms with their time intervals formed with 1:2:4, 1:2:3, and 1:2.5:3.5 ratios. We took advantage of fMRI to make selective measurement of brain activations during the memory delay period, which would reflect the neural activation underlying the internal representation of rhythm.
MATERIALS AND METHODS
Subjects
Six normal subjects participated in the study (four males and two females; age 27-44; all right-handed). None of them were professional musicians. Informed consents were obtained from all the subjects before the study. The experimental protocol was approved by the ethics committee of the Communications Research Laboratory (Kobe, Japan).Behavioral paradigm
A sequence of seven short tone bursts was presented to the subjects. Each tone had the same frequency: 1 kHz; rise-fall time, 5 msec; plateau, 20 msec; and intensity, 95 dB. The six intervals marked off by the onsets of the seven tones were determined to comprise two short (S), two intermediate (I), and two long intervals (L), where the S, I, and L were related with 1:2:4 (1:2:4 rhythm), 1:2:3 (1:2:3 rhythm), or 1:2.5:3.5 (1:2.5:3.5 rhythm) ratios (Fig. 1). By taking all the possible orders of the two Ss, Is, and Ls (e.g., SISLLI), we created 90 (6C2 × 4C2 × 2C2) sequences for each of the three types of the rhythm sequence. The duration of the rhythm sequence, as measured by the time interval from the onset of the first tone to the onset of the last tone, was randomly chosen from 3220, 3360, 3500, 3640, and 3780 msec.
The subjects were asked to hold the presented rhythm sequence in memory for a period of 10.8 sec and then to reproduce it by pressing a button with the right index finger. Instruction was given to keep the relative relations of the time intervals, as well as the absolute time intervals of the presented sequence. The memory performance was assessed based on the reproduced sequence of button presses. Three measures were used for this purpose: order of the time intervals classified as S, I, and L; ratio of the S, I, and L; and duration of the sequence. Order. The six time intervals of button pressing in the reproduced sequence were classified into two Ss, two Is, and two Ls. The order of the three classes of the time intervals (e.g., SISLLI) was compared with that of the presented tone sequence. If the order was different, the trial was regarded as an error and was eliminated from the following behavioral data analysis. Ratio. Subsequently, we calculated the ratios of the button press intervals of the reproduced sequence. The mean of the two Is and the mean of the two Ls of reproduced rhythm was respectively divided by the mean of the two Ss. The ideal ratios would be 2 and 4 for 1:2:4 rhythm, 2 and 3 for 1:2:3 rhythm, and 2.5 and 3.5 for 1:2.5:3.5 rhythm. Duration. Another index for the accuracy of retention was the duration of the sequence. The regression analysis was performed on the duration of the reproduced sequence with that of the presented tone sequence. Ideally, these durations should be correlated linearly with a slope of 1.0 and an intercept of 0. In the present study, we were interested in the rhythm, which can be expressed by the order and ratio. To eliminate the effects of the processes required for retention of absolute time intervals (duration), we also presented the control tone sequences (control), which were formed with seven tones separated by a constant interval. The total duration of the control sequence was randomly chosen from 3220, 3360, 3500, 3640, and 3780 msec to match that of the rhythm sequences. The comparison between the rhythm sequence (order + ratio + duration) and control sequence (duration) would selectively reveal the processes for retention of the rhythm (order + ratio).
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Figure 1. Task procedure. Procedure of a task to examine the short-term memory of rhythm. An experiment consisted of 120 trials. For each trial, the subjects were presented with a sequence of seven tones during the first 4.0 sec and were asked to keep it in memory for 10.8 sec. At the last 1.8 sec of the memory delay period, the scans were performed. During the subsequent 5.2 sec period, the subjects reproduced the maintained sequence by pressing a button. The intertone time intervals of the tone sequence was related with 1:2:4 ratio (1:2:4 rhythm), 1:2:3 ratio (1:2:3 rhythm), or 1:2.5:3.5 ratio (1: 2.5: 3.5 rhythm), and the total duration of the sequence was varied across trials ranging from 3220 to 3780 msec. The control sequence consisted of seven tones separated by a fixed intertone interval.
fMRI data acquisition
Before the fMRI experiments, the subjects underwent practice sessions using 10 of the 90 sequences for each type of the rhythm sequence. For fMRI experiments, the rhythm sequences were chosen from the remaining 80 sequences. Each sequence was used only once in each experiment. An experiment comprised 120 trials, each of which is composed of the tone presentation period (4 sec), memory delay period (10.8 sec), followed by the reproduction period (5.2 sec) (Fig. 1). The subjects fixated their gaze at the center spot on the screen and were not allowed to move any body parts or to vocalize the rhythms throughout the experiment, except for button presses during the reproduction period. The motion of the subject's head was minimized by using a strap around the forehead, bite bar, and ear fixation blocks. In the tone presentation period, the tone sequence was delivered to a headphone through a pair of plastic tubes (length, 180 cm), and the subjects kept the sequence in memory during the memory delay period. At the end of the delay period, a brief high-pitched tone (frequency, 2 kHz; duration, 30 msec) was presented, which served as a cue to reproduce the presented tone sequence with button presses. The subjects had to reproduce the sequence within the 5.2 sec reproduction period, after which the next trial started. For measurement of brain activation, we used Siemens (Erlagen, Germany) Vision 1.5 tesla scanner equipped with a circular polarized head coil. Fourteen slices of T2*-weighted gradient-echo echo-planar images [repetition time (TR), 20 sec; echo time (TE), 66 msec; inversion time (TI), 300 msec; flip angle (FA), 90 degree] were collected within the 1.8 sec period at the end of the TR with the use of clustered volume acquisition (Edmister et al., 19991:2:3 rhythm × 10 trials
fMRI data analysis
Location of active areas. First, we performed a statistical parametric analysis on the functional images of the six subjects to identify the brain areas associated with retention of rhythms. For each experiment, the 120 functional images were realigned to the first image of each subject and were stereotaxically normalized into the T2 template of the standard brain using the software of SPM96 (Welcome Department of Cognitive Neurology, London, UK, http://www.fil.ion.ucl.ac.uk) (Friston et al., 1995
RESULTS
Behavioral data
The memory performance was assessed based on the order, ratio, and duration of the reproduced rhythms (examples shown in Fig. 2a). None of the six subjects showed error rates above 10%. The error rates were not significantly different between 1:2:3 and 1:2:4 rhythms (experiment 1, t(1,5) =
2.0; p > 0.1) but were significantly larger for 1:2.5:3.5 rhythm than 1:2:4 rhythm (experiment 2, t(1,5) =
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Figure 2. Behavioral data. a, Three examples of the presented tone sequence (circles with lines) and the reproduced sequence (crosses) obtained from one subject are shown for 1:2:4, 1:2:3, and 1:2.5:3.5 rhythms and control. b, Summary of the behavioral data from six subjects. Left, Reproduced ratios shown respectively for the six subjects. Each X represents the mean value for one subject. Middle, Right, Means of the slopes (middle) and intercepts (right) of the regression lines between the total duration of reproduced and presented sequences. Error bars indicate the SEs. Data from experiment 1 (top) and experiment 2 (bottom).
fMRI data
Location of active areas
Comparisons of 1:2:4, 1:2:3, and 1:2.5:3.5 rhythms with control revealed brain areas associated with retention of the rhythm components (Table 1). 1:2:4 rhythm was tested twice (experiments 1 and 2), and activations in the left premotor and parietal areas were consistently observed, confirming the reproducibility of the finding (Fig. 3a). In addition, almost the same set of brain areas was active for 1:2:3 rhythm. In contrast, the activation pattern for 1:2.5:3.5 rhythm was completely different; the right prefrontal, premotor, and parietal areas were active. The anterior part of the right prefrontal cortex was active only for 1:2.5:3.5 rhythm but not for 1:2:4 and 1:2:3 rhythms (Fig. 3b). The analysis of individual subjects showed that this prefrontal activation focus was located within the anterior part of the middle frontal gyrus close to the inferior frontal gyrus (Fig. 4b, blue circle). Additional activation foci were found in the cerebellum; the right anterior lobe was active for 1:2:4 and 1:2:3 rhythms but not for 1:2.5:3.5 rhythm, whereas the bilateral cerebellar posterior lobe was active for 1:2.5:3.5 rhythm but not for 1:2:4 rhythm (Fig. 3b). Only the right posterior lobe was active for 1:2:3 rhythm. Individual subject analysis showed that the activation foci in the cerebellar anterior lobe were located in the quadrangular lobule [corresponding to hemispheric lobule IV (HIV)-HV] (Fig. 4a, pink circle), whereas the foci in the posterior lobe were located within the simplex lobule and the superior semilunar lobule of the cerebellum (corresponding to HVI-crus I of HVIIa) (Fig. 4b, green circle).
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Table 1. Stereotaxic coordinates and Z scores of active areas
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Figure 3. Statistical parametric analysis. a, Statistical parametric maps (SPM{z}) of the six subjects when 1:2:4, 1:2:3, and 1:2.5:3.5 rhythms were respectively compared with control. The foci of significantly increased activities were rendered onto the surface template of the standard brain as implemented in SPM96 (Welcome Department of Cognitive Neurology, London, UK) and are shown in red. b, Activation foci in a are shown in three slices at 18 mm above (left), 16 mm below (middle), and 22 mm below (right) the level of the AC-PC line; the prefrontal cortex (blue circle), cerebellar anterior lobe (pink circle), and cerebellar posterior lobe (green circle). White dotted lines in the cerebellum indicate the primary fissure that separates the anterior and posterior lobes of the cerebellum. The right corresponds to the right hemisphere.
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Figure 4. Individual subject analysis. The distribution of the interval ratios of the reproduced rhythms, shown as histograms and rasters. Data are shown for 40 trials of 1:2:4 (a) and 1:2.5:3.5 (b) rhythms in experiment 2. Abscissa of the histogram and raster represents the reproduced ratio. The smaller ratios are shown in blue, and larger ratios are shown in red. For the raster display, trials have been sorted such that the smaller ratios are arranged in the decrementing order from top to bottom. The ratios for the presented rhythms are indicated by the two vertical dotted lines. The activation maps for each subject are shown in three slices in which significant activations are shown in orange. The right corresponds to the right hemisphere. White dotted lines in the cerebellum indicate the primary fissure. a, Activation pattern for 1:2:4 rhythm. The left premotor cortex (yellow circle) and the right cerebellar anterior lobe (pink circle) were consistently active, except for subject 2. b, Activation pattern for 1:2.5:3.5 rhythm. Note the difference in the ratio distribution and activation patterns across the subjects. For the premotor cortex (yellow circle), the right side was active in subjects 1-4, whereas the left side was active in subjects 5 and 6. The prefrontal cortex (blue circle) was active in subjects 1-5, most prominently in subjects 1 and 2. The cerebellar posterior lobe (green circle) was bilaterally active in subjects 1-3, whereas the right cerebellar anterior lobe (pink circle) was active in subjects 4-6.
Correlation of activation with memory performance
As shown in Figure 2b, the memory performance for 1:2:4 and 1:2:3 rhythms was not different across the six subjects, whereas that for 1:2.5:3.5 rhythm considerably differed with respect to its reproduced ratios. The reproduced ratio for 2.5 ranged from 2.15 to 2.45, and that for 3.5 ranged from 3.52 to 3.92 among the six subjects. To further analyze the performance of each subject, we plotted the reproduced ratios for the 40 trials for 1:2:4 and 1:2.5:3.5 rhythms (experiment 2) in histograms and rasters (Fig. 4). Histograms for 1:2:4 rhythm revealed two peaks of the reproduced ratios at 2 and 4 for all the six subjects (Fig. 4a). On the other hand, for 1:2.5:3.5 rhythm, the peaks were found at 2.5 and 3.5 for subjects 1-3, whereas additional two peaks were found at 2 and 4 for subjects 4-6 (Fig. 4b). For subject 6, the peaks at 2 and 4 were higher than those at 2.5 and 3.5. The results indicated that the increased variance in the reproduced ratios and deviation of them from the original ratios for 1:2.5:3.5 rhythm were because of these additional peaks. Furthermore, rasters in the figure have shown that the subjects reproduced the rhythms in either 1:2.5:3.5 or in 1:2:4 ratios. Whenever the subject reproduced the 1:2.5 ratio as 1: 2, he reproduced the 1:3.5 ratio as 1:4 in the same trial. The proportion of the two types of reproduction, 1:2.5:3.5 or 1:2:4 ratios, in the 40 trials was varied across the subjects. Looking into the activation maps of each subject for 1:2:4 rhythm, the active areas were found in the left premotor cortex and the right cerebellar anterior lobe but not in the prefrontal cortex, consistent across the six subjects (Fig. 4a). In contrast, for 1:2.5:3.5 rhythm, subjects 1-3 showed prominent activation in the right prefrontal cortex, right premotor cortex, and the bilateral cerebellar posterior lobe (Fig. 4b), whereas subjects 5 and 6 showed activation in the left premotor cortex and the right cerebellar anterior lobe. Thus, the brain activation patterns of subjects 5 and 6, who reproduced the 1:2.5:3.5 rhythm in 1:2:4 ratio, were quite similar to those when 1:2:4 rhythm was presented (Fig. 4a). This finding suggests that the brain activation pattern depends on the ratios of the reproduced rhythms rather than the ratio of the presented rhythms.
DISCUSSION
Two modes of neural representation for rhythm
Earlier psychological studies have, based solely on the behavioral data, proposed two types of rhythm representation depending on the interval ratio of the rhythm (Essens, 1986
The present study used three types of rhythm whose interval ratios were expressed as 1:2:4, 1:2:3, and 1:2.5:3.5, respectively. According to the theory proposed in the psychological literature (Povel, 1984
Our functional imaging data indicated that the brain activation patterns for 1:2:4 and 1:2:3 rhythms were quite similar but were completely different from that for 1:2.5:3.5 rhythm. First, the right prefrontal cortex was active for 1:2.5:3.5 rhythm but not for 1:2:4 and 1:2:3 rhythms. Second, the cerebellar posterior lobe was bilaterally active for 1:2.5:3.5 rhythm, whereas the right cerebellar anterior lobe was active for 1:2:4 and 1:2:3 rhythms. Third, the right hemisphere was predominantly active for 1:2.5:3.5 rhythm, whereas the left side was more active for 1:2:4 and 1:2:3 rhythms. Considering that retention of 1:2.5:3.5 rhythm was more difficult than 1:2:4 and 1:2:3 rhythms (as shown in the increase in the error rate), the difference in the brain activation pattern could reflect the level of attention required for the memory task. We think that this is unlikely, however, because different sets of brain areas were activated in these conditions, some areas showing clear double dissociation. Instead, the results suggest the presence of two distinctive neural representations of rhythm.
Prefrontal cortex
The prefrontal cortex has been regarded as the key structure for working memory, and its activity was shown to reflect the on-line processing of memorized materials (Funahashi et al., 1989
In contrast, the absence of the prefrontal activation for 1:2:4 and 1:2:3 rhythms may suggest that metrical representation does not require additional monitoring processes relative to the control sequence. In metrical representation, the maintenance of a single time interval alone allows to specify all the other time intervals of a rhythm.
Cerebellum
We found a clear double dissociation between the cerebellar anterior and posterior lobe activations, the former being active for 1:2:4 rhythm, and the latter being active for 1:2.5:3.5 rhythm. The anterior lobe of the cerebellum, especially HIV-HV, is related to the ipsilateral upper limb movements (Nitschke et al., 1996
In contrast, the cerebellar posterior lobe has been shown to be related to explicit temporal representation (Ivry et al., 1988
Right versus left hemispheric predominance
We found that metrical representation for 1:2:4 or 1:2:3 rhythms was predominantly associated with left hemispheric activation, whereas the nonmetrical representation for 1:2.5:3.5 rhythm was associated with right hemispheric activation. Previous clinical studies have shown that rhythm deficits were found after left hemispheric lesions, especially when the left premotor and parietal areas were damaged (Brust, 1980
Although we used auditory stimuli for presenting rhythms, the temporal lobes did not show significant activation; only a small portion on the right side was active for 1:2.5:3.5 rhythm. The frontoparietal network active in the present study would, thus, reflect the supramodal mechanism for rhythm processing, as suggested by Mavlov (1980)
To summarize, we have shown that there are two modes of neural representation for rhythm. Their selection depends on the interval ratios of the rhythm or, more precisely, on the strategy used for encoding the rhythm, metrical or nonmetrical. Nonmetrical strategy may require explicit processing for the individual time intervals, whereas metrical strategy may operate automatically, and possibly implicitly, to allow hierarchical encoding of the whole rhythm. In this regard, the right and left hemispheric dissociation observed in the nonmetrical and metrical rhythm processing may be closely related to the finding of Hazeltine et al. (1997)
FOOTNOTES Received May 3, 1999; revised Aug. 26, 1999; accepted Sept. 3, 1999.
This study was supported by Japan Society for the Promotion of Science (JSPS) Research for the Future program and Basic Research System Core. K.S. was supported by JSPS Research Fellowship for Young Scientists. We are grateful to Hiroshi Imamizu and Mitsuo Kawato at Japan Science and Technology Corporation for their cooperation with SPM analysis. We are also grateful to Haruo Uesugi at Department of Neurology, University of Tokyo, who is a professional musician, for his helpful advice on musical theory.
Correspondence should be addressed to Katsuyuki Sakai, Department of Physiology, Juntendo University, School of Medicine, 2-1-1 Hongo, Bunkyo-ku, Tokyo 113, Japan. E-mail: katz{at}med.juntendo.ac.jp.
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